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Real are one point ahead of arch-rivals Barcelona, who can regain their position on top if they beat Malaga later in the day.
Argentinean in-form striker Higuain gave Real the lead just before the half-hour mark when he latched onto a through pass from Marcelo before firing a low shot into the bottom corner.
He doubled their advantage on 42 minutes after being set up by central defender Ezequiel Garay.
Midfielder Ayoze gave Tenerife a lifeline when he headed home early in the first half after capitalizing on a mistake by Real keeper Iker Casillas.
Brazilian playmaker Kaka restored Real's two-goal cushion few minutes later before Cristiano Ronaldo converted a penalty on 80 minutes to add the fourth.
Substitute Raul, who replaced Higuain, completed the rout in stoppage time.